  Brief description of the algorithm for computation of 3D 
displacement caused by the non-tidal ocean pressure loading.
The computation procedure follows these steps:

1) Non-tidal oceanic pressure loading is computed using the bottom 
pressure field at an equi-angular latitude/longitude grid with 
resolution 5401x10800 derived from the output of the numerical 
model of oceanic circulation.

  2) The land/sea mask was derived from the MOD44W model using the 
following procedure: a) original MOD4WW mask was re-sampled to 
resolution 86400x43000 over longitude and latitude with Closed 
basins, such as lakes and the Caspian Sea are considered land;
b) spherical harmonics transform of degree/order 21,599 was performed;
c) the spherical harmonics transform of the mask was multiplied
by Blackman window of degree/order 2,699; d) the inverse spherical
harmonics transform of degree/order 2,699 was performed over the 
results to for, the final bandlimited land-sea mask with resolution 
5401x10800 over latitude/longitude (2'x2'or ~3.7 km). The land-sea 
mask at a given cell is a number in a range -0.0004 to 1.0006 that 
is equal to the ratio of the area covered by land (i.e. 
non-ocean in this context) to the total area of the cell.
 
  3) The Love numbers have been computed using REAR software,
Melini D., Gegout P., Spada G, King M. (2014), "REAR --  a regional 
Elastic Rebound  calculator. User manual for version 1.0", available 
on-line at  http://hpc.rm.ingv.it/rear. Earth reference model STW105 
(Kustowski et al., 2007), which is an update of PREM (Dziewonski and 
Anderson, 1981) was used. The elastic rheology of the Earth derives 
from the waves speed and the density, with the top  three kilometers 
of oceanic water replaced by underneath rock materials. The model 
defines the Earth (hydrostatic) equilibrium, the pressure and the 
gravity inside the Earth; numerical computations allow to take 
compressibility into account. The Love numbers are computed in the 
coordinate system with the centrum at the center of mass of the total 
Earth: solid Earth, ocean, and the atmosphere. Therefore, loading 
displacements computed with using such Love numbers are the 
displacements with respect to the center of mass of the total Earth 
that includes the mass of the ocean.

  4) The ocean bottom pressure is multiplied by the land-sea mass
function. Then the spherical harmonic transform of degree/order 2699
is performed. The spherical harmonics expansion coefficients S(k,n) 
are scaled by factors 

   Sv(k,n) = 3*H_n/(2*n+1)/(mean_dens*mean_grav) * S(k,n) (vertical)
   Sh(k,n) = 3*L_n/(2*n+1)/(mean_dens*mean_grav) * S(k,n) (horizontal)

where H_n and L_n are loading Love numbers, k is order, n is degree, 
mean_dens is the mean density of the Earth and mean_grav is the mean 
gravity acceleration at the sea level. Two sets of scaled spherical 
harmonics are generated: vertical Sv(k,n) and horizontal Sh(k,n).

  5) Then the mass loading in the vertical direction is computed by the
inverse spherical harmonics transform of Sv. The horizontal displacements 
in the northern and eastern directions are computed as a partial 
derivative of the inverse spherical harmonics transform of Sh. The result
of these spherical harmonics transform is a global 3D displacement
field at 2'x2' (5401x10800) equi-angular grid.

  6) Sampling correction to the displacement field was applied. The 
sampling correction was computed as a product of surface pressure by the 
differences of the band-limited windowed land-sea mask with resolution 
15"x15" (464x464m) and the band-limited windowed land-sea mask with 
resolution 2'x2. The sampling correction mitigates artifacts of using 
a band-limited windowed mask truncated at degree/order 2,699 instead of 
using the true mask, which is not bandlimited to degree/order at least 
100,000. The sampling correction affects loading within 30 km of the coastal 
line.

  The maximum error of displacements due to approximation used in the 
computational procedure is below 0.2mm. The main error source in loading
displacement is the uncertainty of the model.

References:

   Petrov, L., The International Mass Loading Service, 
      Proceedings of the Reference Frames for Applications in 
      Geosciences Symposium, held in Luxembourg in October 2014, 2015. 
      DOI: 10.1007/1345_2015_218, http://arxiv.org/abs/1503.00191

   Petrov L., J.-P. Boy, "Study of the atmospheric
      pressure loading signal in VLBI observations", Journal of
      Geophysical Research, 10.1029/2003JB002500, vol. 109,
      No. B03405, 2004.
